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arxiv: 1907.06280 · v1 · pith:4DHU723Hnew · submitted 2019-07-14 · ✦ hep-th

Noncommutative Gauge Theories and Gravity

G. Manolakos , P. Manousselis , G. Zoupanos This is my paper

Pith reviewed 2026-05-24 21:30 UTC · model grok-4.3

classification ✦ hep-th
keywords theoriesgaugegravitynoncommutativebrieflydimensionsfourprocedure
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The pith

The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors first recall standard ways to write general relativity as a gauge theory in three and four dimensions and extend the same logic to Weyl gravity. They then turn to noncommutative spaces, where coordinates do not commute, and review their own recent papers that build gravity models inside that framework. The goal is to keep the gauge-theory structure while incorporating noncommutativity, which is sometimes proposed as a way to handle quantum effects at very small distances. Because the text is a review, it organizes and connects existing constructions rather than deriving new equations or presenting fresh data.

Core claim

Gravity models can be constructed as gauge theories on noncommutative spaces, as shown in the authors' recent works reviewed here.

Load-bearing premise

The assumption that the noncommutative deformation of spacetime preserves enough structure to recover classical gravity while allowing a consistent gauge-theory formulation (invoked when moving from the commutative review to the noncommutative constructions).

read the original abstract

First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a gauge-theoretic approach. Also, the procedure is applied for the case of the Weyl gravity, too. Then, after reminding briefly the formulation of gauge theories on noncommutative spaces, we review our most recent works in which gravity models are constructed as gauge theories on noncommutative spaces.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a review that first recalls the gauge-theoretic formulations of General Relativity and Weyl gravity in three and four dimensions in the commutative case, including the procedures used to recover the standard results, and then summarizes the formulation of gauge theories on noncommutative spaces together with the authors' recent constructions of gravity models in that setting.

Significance. If the constructions reviewed hold, the paper provides a compact compilation of how gauge-theoretic gravity extends to noncommutative deformations while recovering classical limits. Its value lies in organizing the authors' prior results into a single narrative; no new derivations, theorems, or computations are presented.

minor comments (2)
  1. Abstract: the transition sentence from the commutative review to the noncommutative constructions does not indicate which specific noncommutative models or dimensions receive the most attention, making the scope of the review harder to assess at first reading.
  2. The manuscript would benefit from an explicit list or table in the introduction or conclusion that maps each reviewed noncommutative construction to its corresponding commutative counterpart and to the original reference, improving traceability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their review and recommendation of minor revision. No specific major comments were provided in the report, so we will incorporate any minor editorial improvements in the revised version while preserving the review nature of the manuscript.

Circularity Check

0 steps flagged

No significant circularity; review paper without internal derivation

full rationale

The manuscript is a review that first recalls standard commutative gauge-theoretic formulations of gravity (including Weyl gravity) and then summarizes the authors' prior constructions on noncommutative spaces. No new derivation, theorem, prediction, or first-principles result is presented whose steps can be examined. The abstract and structure explicitly frame the work as a review of existing results rather than a self-contained derivation chain. No equations or claims reduce by construction to inputs within this paper. Self-citations are present by design of a review but do not create load-bearing circularity here, as the paper makes no independent claim whose validity depends on unverified self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is a review and introduces no new free parameters, axioms, or invented entities in the provided abstract; all content rests on standard gauge-theory and general-relativity assumptions plus the authors' prior constructions.

axioms (1)
  • domain assumption Gauge theories can be formulated on noncommutative spaces while retaining a consistent notion of curvature and action
    Invoked when the review transitions from commutative to noncommutative constructions.

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discussion (0)

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